{
 "cells": [
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   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<a href=\"https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv\" target=\"_blank\"><img align=\"left\" src=\"data/cover.jpg\" style=\"width: 76px; height: 100px; background: white; padding: 1px; border: 1px solid black; margin-right:10px;\"></a>\n",
    "*This notebook contains an excerpt from the book [Machine Learning for OpenCV](https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv) by Michael Beyeler.\n",
    "The code is released under the [MIT license](https://opensource.org/licenses/MIT),\n",
    "and is available on [GitHub](https://github.com/mbeyeler/opencv-machine-learning).*\n",
    "\n",
    "*Note that this excerpt contains only the raw code - the book is rich with additional explanations and illustrations.\n",
    "If you find this content useful, please consider supporting the work by\n",
    "[buying the book](https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "<!--NAVIGATION-->\n",
    "< [9. Using Deep Learning to Classify Handwritten Digits](09.00-Using-Deep-Learning-to-Classify-Handwritten-Digits.ipynb) | [Contents](../README.md) | [Implementing a Multi-Layer Perceptron (MLP) in OpenCV](09.02-Implementing-a-Multi-Layer-Perceptron-in-OpenCV.ipynb) >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
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   "source": [
    "# Understanding Perceptrons\n",
    "\n",
    "In the 1950s, American psychologist and artificial intelligence researcher Frank Rosenblatt invented an algorithm that would automatically learn the optimal weight coefficients $w_0$ and $w_1$ needed to perform an accurate binary classification: the perceptron learning rule.\n",
    "\n",
    "Rosenblatt's original perceptron algorithm can be summed up as follows:\n",
    "\n",
    "1. Initialize the weights to zero or some small random numbers.\n",
    "2. For each training sample $s_i$, perform the following steps:\n",
    "   1. Compute the predicted target value $ŷ_i$.\n",
    "   2. Compare $ŷ_i$ to the ground truth $y_i$, and update the weights accordingly:\n",
    "      - If the two are the same (correct prediction), skip ahead.\n",
    "      - If the two are different (wrong prediction), push the weight coefficients $w_0$ and $w_1$ towards the positive or negative target class respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implemeting our first perceptron\n",
    "\n",
    "Perceptrons are easy enough to be implemented from scratch. We can mimic the typical OpenCV or scikit-learn implementation of a classifier by creating a `Perceptron` object. This will allow us to initialize new perceptron objects that can learn from data via a `fit` method and make predictions via a separate `predict` method.\n",
    "\n",
    "When we initialize a new perceptron object, we want to pass a learning rate (`lr`) and the number of iterations after which the algorithm should terminate (`n_iter`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
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   "source": [
    "import numpy as np\n",
    "class Perceptron(object):\n",
    "\n",
    "    def __init__(self, lr=0.01, n_iter=10):\n",
    "        \"\"\"Constructor\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        lr : float\n",
    "            Learning rate.\n",
    "        n_iter : int\n",
    "            Number of iterations after which the algorithm should\n",
    "            terminate.\n",
    "        \"\"\"\n",
    "        self.lr = lr\n",
    "        self.n_iter = n_iter\n",
    "        \n",
    "    def predict(self, X):\n",
    "        \"\"\"Predict target labels\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        X : array-like\n",
    "            Feature matrix, <n_samples x n_features>\n",
    "            \n",
    "        Returns\n",
    "        -------\n",
    "        Predicted target labels, +1 or -1.\n",
    "        \n",
    "        Notes\n",
    "        -----\n",
    "        Must run `fit` first.\n",
    "        \"\"\"\n",
    "        # Whenever the term (X * weights + bias) >= 0, we return\n",
    "        # label +1, else we return label -1\n",
    "        return np.where(np.dot(X, self.weights) + self.bias >= 0.0,\n",
    "                        1, -1)\n",
    "        \n",
    "    def fit(self, X, y):\n",
    "        \"\"\"Fit the model to data\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        X : array-like\n",
    "            Feature matrix, <n_samples x n_features>\n",
    "        y : array-like\n",
    "            Vector of target labels, <n_samples x 1>\n",
    "        \"\"\"\n",
    "        self.weights = np.zeros(X.shape[1])\n",
    "        self.bias = 0.0\n",
    "        for _ in range(self.n_iter):\n",
    "            for xi, yi in zip(X, y):\n",
    "                delta = self.lr * (yi - self.predict(xi))\n",
    "                self.weights += delta * xi\n",
    "                self.bias += delta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating a toy dataset\n",
    "\n",
    "To test our perceptron classifier, we need to create some mock data. Let's keep things simple for now and generate 100 data samples (`n_samples`) belonging to one of two blobs (`center`s), again relying on scikit-learn's `make_blobs` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y = make_blobs(n_samples=100, centers=2,\n",
    "                  cluster_std=2.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adjust the labels so they're either +1 or -1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "y = 2 * y - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
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DQkJ9PTlHPi+HD5fzxBPr+P77I2eOeXtruffeftxxRy+p++Zh5L1FNEdMTAxAsybySrLm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\n+LD/DxPimf3PF/bvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2197026c780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], s=100, c=y);\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')\n",
    "plt.savefig('perceptron-data.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting the perceptron to data\n",
    "\n",
    "We can instantiate our perceptron object similar to other classifiers we encountered with\n",
    "OpenCV:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "p = Perceptron(lr=0.1, n_iter=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "p.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the learned weights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.20091094, -0.4798926 ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20000000000000001"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we plug these values into our equation for $ϕ$, it becomes clear that the perceptron learned\n",
    "a decision boundary of the form $2.2 x_1 - 0.48 x_2 + 0.2 >= 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating the perceptron classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "accuracy_score(p.predict(X), y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def plot_decision_boundary(classifier, X_test, y_test):\n",
    "    # create a mesh to plot in\n",
    "    h = 0.02  # step size in mesh\n",
    "    x_min, x_max = X_test[:, 0].min() - 1, X_test[:, 0].max() + 1\n",
    "    y_min, y_max = X_test[:, 1].min() - 1, X_test[:, 1].max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                         np.arange(y_min, y_max, h))\n",
    "    \n",
    "    X_hypo = np.c_[xx.ravel().astype(np.float32),\n",
    "                   yy.ravel().astype(np.float32)]\n",
    "    zz = classifier.predict(X_hypo)\n",
    "    zz = zz.reshape(xx.shape)\n",
    "    \n",
    "    plt.contourf(xx, yy, zz, cmap=plt.cm.coolwarm, alpha=0.8)\n",
    "    plt.scatter(X_test[:, 0], X_test[:, 1], c=y_test, s=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x219721500b8>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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l/Qv4GUhJS0srSktLuwR4GDg+LS1tJ3Dcbz8L0Sk/s8LoeB3JI1VGxekw6MGo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\nERFxkZIxERERERf9P0z/zU/YpzbHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21972140160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plot_decision_boundary(p, X, y)\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applying the perceptron to data that is not linearly separable\n",
    "\n",
    "Since the perceptron is a linear classifier, you can imagine that it would have trouble trying\n",
    "to classify data that is not linearly separable. We can test this by increasing the spread\n",
    "(`cluster_std`) of the two blobs in our toy dataset so that the two blobs start overlapping:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X, y = make_blobs(n_samples=100, centers=2,\n",
    "                  cluster_std=5.2, random_state=42)\n",
    "y = 2 * y - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x219721c9fd0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PPtqPpUuvZ9Cgdri7u+Hnp+fBB/uwcuVE+vZtvNYpjUZD376OZzr26VPVCgeQnJxPRYX9\npSveeGMneXl1j+1LSyt0+JyrV6eSn+94fKCzFRdX8tprO5k5c32NYvf48SLuv/9bFi3aQ2mpLPUh\nRGsl3alCiBr8/XWMHBnFiBEdyc4uxs1NQ0iIB5pGHutvtVq5/vpYFi7cYTdu+PDo6v8vKXFcWOXm\nlmE0XlorWtXv6vqTGw4fzmfRol11np8//3euuy6WHj1kjJoQrZG0xAkhbPL39yI83JPQ0MYv4M5J\nSgpg9uyBdZ7/v/8bSlzc+fXGgoK8HF4zPj4Ab++6v5/Gxjpe+mLcuHiCgvQO45xJo9GwalWaw7hv\nvz2Kpqn+AYUQTiVFnBDCaby8tEyf3o3337+e7t1Dqo/36xfOxx+PZfLkTnh4aKuPJyUFEBhof0ze\nQw/1xWCou4hLSPDn8ssj6zyv0cBtt3VpEQsN792b4zBm/37HMa2VFK+itZPu1BbEaLRgNlvx8tI6\nDhaihfD1defqq6MYOHAsOTnlaDQawsI88fGp/fEUEeHFwoVXc8cdq6oXBr7QiBHtGTjQ/n6dvr7u\nvPzyCGbMWMeePTULHK1Ww5tvXkPXrkGX9ks1k9hYf3788YTDmLbEXFZGYWoqJ3/8kbyUFAITEoga\nNgy/uDi0Xo5bcoVoSaSIawGOHSth69ZTLFmyj4oKMyNHdmDcuHiSkvxlLSvRavj56fDzq72o7x8N\nHRrBihU38uqrv/Ptt0cBCA314pFH+jN6dAxhYY5nz3bo4MPSpddz4MAZVqxIIT+/gqFDo7j88iji\n4gwtohXOarUyYUICS5bssxt33XWx1RNDWjtTQQG7//tfts+fX+tcv4ceovu996KXWbSiFdG04je3\nNSMjw9k5XLIDBwq45Zavyc0tq3Fco4HXXruKceNiGlTIGQwGioqKGjvNFk/uS22ufk8qKixkZJRi\nMlkICNDXq3iz5VyXW30/C13pvhQUmHjqqc18+WWKzfO33tqZOXMG2+1ebiyucF9SPv2UjbNm1Xl+\n5Pz5xE+a1IwZucZ9cTVyT2yLjIyEBs6okmYcF5adXcHUqatrFXBQtZbVgw+uZ//+fCdkJoTzeXi4\nERvrS6dOfhddwEFV8dZSv8z6++uYM2cIs2cPxMfnfCumwaDn6acH8+STA5ulgKuvc/vUNoXy06f5\n5cUX7cb88s9/Up6d3STPL4QzuM67W9Ry6FBejbWf/shqhc8+S6ZHj8uQhdKFaJtCQz148MFeTJyY\nyIkTxWg0EB3tS1SUt7NTA6p2wTh6tJht207z+++ZBAR4MHJkBzp1CiAgoPFmAJdkZFB6+rT9mMxM\nSjIy8AwNtRsnREshRZwL278/12HMunXpPPpo30b9MBRCtDzR0d5ER7tG4XaO2Wxlw4aTzJixDqPx\n/KLDCxbsYOjQKF55ZUSjFZtWSz3XBmyhra5C2CLtNy5Mr3c8C9Xd3Q03N9cfhC2EaHv27ctj+vQ1\nNQq4czZvPsmcOVsoK2ucHSW8w8PR+9lfA9DD3x/vsLBGeT4hXIEUcS6sR48QhzGTJ3fG319a4YQQ\nrsVstvLBB/uxWOpu+Vq9OpXUVMfboNWHT3Q0/exMagDo//DDeEdFNcrzCeEKpIhzYYmJ/lx2Wbs6\nz3t5uXPttTEtdlC2EKL1ys2tqHPW7IXqs5dtfVitVhImTiRh/Hib5xNvvJH4G2+Uz0vRqsiYOBfm\n56fj1Vev5C9/Wc+2bVk1zhkMepYuvZ5OnRxvISSEEM3NagWz2fE4NXstdQ3lGRrK5S++SNcpUzjw\n0UcUpKYSEB9P58mTCezcGX1AQKM9lxCuQIo4F9e+vQ/vvTeaw4cL2Lz5BGVllfTtG06PHiEuN4hZ\nCCHOCQzUc+WVHfjmG/v7u7Zvb7B7vqH0AQGEX3YZEYMHYzEacdPrpfVNtFpSxLUAgYF6Bg4MZeDA\nUDQajXwgCSFcnl7vxowZPe0Wcf37R5CQ0DQ7KFitVjQ6nXxeilZNxsS1MPKBJBpKNgEXztKzZzBz\n5w63eS4+3p9XX73SpRYjFqKlkXePEK3QmTMVHDqUz5YtGRiNFvr3D6dbt2DatZMNwEXz8fTUcvPN\nifTqFcaqVUf46acMfH11TJ3ajV69QuX1KMQlkiJOiFYmPb2Ye+5Zy/79Z2ocDwnx4oMPxtCjR6CT\nMhNtkYeHGz16BNKz5wCMRgvu7hqkcViIxiHdqUK0Irm5Fdx9d+0CDiAnpwxFWUFaWt1buQnRVKxW\nKzqdFHBCNCYp4oRoRQ4dyufAgdoF3DmFhUa2bMmo17WsVquMpxNtnrwHhCuT7lQhWgmNRsNPP51w\nGPfhhweYNCkBvd72d7j8fBPJyfn8+useyspM9OoVSvfuwURGypI2om2wmEwUp6eTtW0b+ampGKKj\niRg4EENsLFpPT2enJ0Q1KeKEaEUqKhwvrlpZaeGPe4WbTBYKC00UF1fy3HM/s3Zteo3zAQEefPDB\nGPr0CW7EbIVwPZUlJaR8+imb//53rH94o/SZOZOe990niwYLlyHdqUK0ElarlYEDIxzGXXddLF5e\nWgCKiyv5+ecs7r9/A1dd9SmTJ68kLi6AZ54ZgsFwfk/e/PwKbr31a1JSiposfyFcQeaWLfz4t7/V\nKuAAdixYQNrXXzshKyFskyJOiFake/dgAgPr7u7RajXV++0WF5t4883d3HzzCr75Jo3s7DKOHi3k\nzTd38tprv/PMM0Pw8jrfWF9cbGLjxmPN8WsI4RTGggK2vvCC3Zhf586l7NSpZspICPukiBOiFYmM\n9OaDD66v0Yp2jlar4e23R5GUVLVC/s6dObz66u82r5OfX8HChTuYPLlLjeMffXSA4uLKxk9cCBdQ\nmpFBXnKy3ZjyvDyKjx9vpoyEsE/GxAnRyvTuHczq1RPZvDmDjz8+gMlk4frrYxk9OpakJH+0Wg3l\n5WbeeGOn3eukpxfU2tfSZLI06oblQrgSW12otljqGSdEU5MiTohWKC7OQFxcEoqSiMVixdtbW+N8\nYaGJ337LdHid8nIzGg2c2+3t6qtjZJsk0Wp5hYbiFRpKWXZ2nTFaDw98IhyPPRWiOUh3qhCtmKen\nW60CDsDNTYOnp+NiTKvVVBdwGg1MnJgg62aJVsszLIwBjz1mN6bH9On4duzYTBkJYZ8UcUK0QcHB\nHtxxR1e7MRoN6PXa6v9/7bWr6NJFllYQrVvMddeReNNNNs9FXn453e+6C9l2QrgKjdXaase3WDMy\n6rcyfVtiMBgoKpJlIv6oMe9LebmZoqJKdDo3AgJ0jXLNpnDoUAFjxnxBWZntiQo33dQJnU5LUJAH\nN9wQT+fOAeh08r1P3kO2tab7YszP58y+fex//33yUlLwjYqi+7RphPTsiUdISIOu1ZruS2ORe2Jb\nZGQkQIO+IcjgFiEaSX6+kR07cli0aCd79uTg56dnxoxejBzZnpgYX2enV0tSkj/Llo1j+vQ15OSU\n1Tj3pz914a9/HYiPjxZvb+0lNTyUl1swmSx4e7ujrd2zK4TL0QcEEHH55YRfdhmW8nLcPDzQuMuf\nS+F6pCWujZFvQLZd6n3Jzzfy0ku/sXTp/lrnQkK8+PTTG+jUye9SUmwymZllHDqUz9GjBXh76+ja\nNZiYGAPh4QGXdE9OnChh69ZMFi/eQ3GxiQEDIpg8uQtdugTg49Ny/yDKe8g2uS+2yX2pTe6JbdIS\nJ4STbNmSabOAA8jJKeOhhzawbNkY/Pxcr3s1IsKLiAgvoF2jXfPIkSImT17JyZPFFxzL55NPDvLE\nE4OYPr1riy7kmltlpZVjx4opLDTi7e1O+/a+1btuCCHaLvkUFeISFRaamDdvm92Y3buzOXKksHrv\n0ZKSSlJTC8nOLkOv1xIX509UlDetoWW8sNDEgw+ur1HAXeill36hd+9Qhg1rvKKxNUtNLeL113fy\n2WeHMJurXh/Dh0fz5JOD6NEjSMbYC9GGSREnxCUqKjKxb1+uw7jMzBIgmOTkQp544gd++eX81j3+\n/h48++wQxoyJwde3Zb8tU1IK2Lmz7nW2AN54Yyf9+4dJa5IDqalFTJz4FdnZNccs/vDDCbZsyWD5\n8gnVXwyEEG2PTDUT4hK5uWnqNWtTp3MjNbWISZNW1CjgAAoKKnjkkY188UUKLb0xrq4WuAv9/HMG\nhYWmZsim5bJYYMmSA7UKuHNMJguzZ38v91GINkyKOCEuUViYJ7fc0tlujE7nRlJSICtXppKba/uP\nMsDzz2/h+PGSxk6xWWm19StoncVotJCcXMDWrVns2JFDXp7RabnYc/JkCUuW7LUbs29fLkeOFDZT\nRkIIV9Oy+22EcAFarYYpU7qhqocwGs02Y2bO7IuHhzuLFu2ye62yskpSUvLp0MGnKVJtFnFx/jW2\n6rLl5puTCAnxbL6kzkpNLWLu3F9ZtSq1Or+4OH9eeGEYl10Wjl7vOt9rS0oqqaiw/Xq6UFGRaxah\nQoim5zqfWEK0YF27BvDxx2MJCqpZmLi5aXjggT7ceWdXzGYLBQUVDq9VUtKyu8fi4gzcemuXOs+7\nu7vxpz91afY149LSirnpphWsXJlao8BMTS1g8uSVbNp0snkTcsDb271eLZa+vq4341kI0TykJU6I\nRqDRwGWXhbFu3SSSk/PIyCjB11dHUlIQsbEGdDoNBQUm4uL8SU0tsHut4ODmb6FqTHq9G4891o+S\nEhMrVqTUOOfjo+N//xtFt27Nv33Xl1+mcPp0aZ3nH3/8e3r1mkR4uGvc/6goH267rQvvvbevzphO\nnYKIi/NvxqyEEK5Eijgh6pCdXc6hQ/mkpOTh4eFO165BxMf725092q6dF+3aedk85++v4+GH+zNz\n5no7j/chMTHwknN3togIL/7972Hcd18vtm3LJD+/gi5dgunRI5j27Zu/qzgzs5xFi3bajcnOLiMl\nJZ/w8IjqY1aTiaK0NPIOH8ZsNOITEYG1e3c0BkNTp4xWC9Om9eCrr46Ql1du47yGuXOHu/TWbkKI\npuVSRZyiKO8AY4EsVVV7nj0WCCwDOgLpgKKqqv2mDCEu0d69edx55zecOlVzksG118bwwguXExnp\nfVHXHTo0kmHDovnxxxO1zun1WhYuvJrQUI+Lurar8fV1p1evIHr1CnJ2KlRUmCkudtxNfWFMeXY2\nuxcuZPc772C1WKqPG6KjGfX22wT27HnR+Zw5Y6SgwIhO50Z4uBc6ne3F3hISDCxfPp65c39lzZq0\n6m7gvn3DmTNnCL17y/IiQrRlrjYm7l1g1B+OPQF8p6pqErABeLLZsxJtSlpaEYryda0CDmDdunSe\nemozRUUXN24tLMyT+fOv5KWXhhMeXlUIurlpmDixE19/fSMDB4ZdUu7CNi8vLYGBjrtJ/f2rCmiL\n0cjuhQvZ9fbbNQo4gKITJ1ihKBQePtzgPHJyKvj00yNcd90XDB36MYMHf8Qjj/zAnj15dU4ESUz0\n4403RrJhg8KXX05g3bpJfPzx9fTrF4JWKyv9CtGWuVQRp6rqZiDvD4fHA++f/f/3gQnNmpRoczZt\nOmF3AsK33x69pGUdwsM9ueOOJNauncQPP9zKTz9N5pVXhtO9e6Csvt9EwsI8efDBvnZjoqJ8SUys\nGl9WnJ7O7nfeqTPWWFRE2qpVDcohN7eCJ5/8kVmzNnDiRNW+kRaLlS++SGbcuC/YsiWrzsfq9W50\n6uTPgAGhdOsW2OIXhBZCNA6XKuLqEKaqahaAqqqZQKiT8xGtWHFxJUuW1D2Q/BxHOxLUR2ioB/Hx\nBjp08KmzO000nuuvjyUx0faECq1Ww/z5IwkOrmqJyzt8uFYL3B/tee89KnId79Rxzq+/ZrF6dZrN\ncyaThfvv/5asrNpj34QQoi7ydU6IC5jNVsrLHa/NVV5e2QzZNL0TJ0o5cOAMqan5BAR40qNHCLGx\nhla5HVZ0tDdLl45h6dL9LF68h7Kyqn/D4cOjefzxgfTseX7snrnccTFlKinBanb8WoGqLwcLFmy3\nG5OTU0Zych7h4a69p6zVbMZUWIjGzQ19QECr2O9XiJaqJRRxWYqihKuqmqUoSgRw2laQoigjgBHn\nflZVFUMzzCBrafR6vdwXG87dFw+PSoYNi+bDD/fbje/SJQRfX180LbT/s7LSzHffpXHXXWtqLRZ7\n553dmT3mCQd3AAAgAElEQVT7MoKDW99rpWtXA//3fyFMm9aDvLwKPD3diY31x2DwqPFvaYiKcnit\n8L598QsNxaMe9ygvL59Dh844jMvNrXDZ15WxpITM7dvZ9+GHHNu4Ea1OR9c77iBu9GjCe/aUz5Y6\nyH2pTe5J3RRFmXPBj5tUVd1kL94VizjN2f/OWQHcCcwFpgJf2XrQ2V900wWHni0qKmqSBFsyg8GA\n3JfaLrwvt96aZLeICw72IinJn+Jix3uEuqo9e/L4059WUllZu8vwvff24u3tznPPDcdorHuLsJas\nXTsP2rU7NwvYVGvmql9CAr5RURSfrHsB4N733YdRo8FYj/eT1WomIMCTzEz7W6p5erq55OvKYjSS\noqp8P3t2jeNbX3iBbfPmMW7ZMmKGD3fJ3J1NPnNrk3tim8FgQFXVOQ15jEuNiVMU5SPgZ6CToijH\nFEWZBrwEXKMoyiHg6rM/C9FkunYN5IUXhtk85+Oj4/33ryMiwvZacC1BZaWV997ba7OAO+ett3Zz\n+HD9x3u1Nh4hIYz63//Q+fraPN/znnsI6Wt/osSFgoL03HtvL7sxOp0bnTq55hqBeQcO1Crgzqks\nLeWbKVPIT7M93k8I0XRcqiVOVdU/1XHq6mZNRLRpnp5abr01ke7dQ/joo/18//0J9Hotd9zRlWuu\n6Uhiop+zU7wkOTnlfPZZst2YykoLhw/n07Hjxa2H1xoE9ezJxJUrSV25kr3vvouptJTwvn3p+5e/\nENSrF3r/hu2UcO21HXnjjR1kZ9tu3Xz88YF07OiCXUwWC8mffWY3pDwvj9N79hA5cmQzJSWEABcr\n4oRwFZ6eWvr3D6F372EUFprQajUEBOhbxSBusxm7rXDn4xzHtHZ+iYn0fvhhukyZgtVsRmcw4B8a\nelHdhjExvnz22Xgef/x7fvnlVPVxX18ds2cP4qab4pt9P9n6qCwp4fimTQ7jcvbulSJOiGYmRZwQ\ndri7awgK0gO0igIOqrb/6t071OEyKZGRtrsS2yKP4PM7I1zKpIOEBANLl47myJFCTp8uRadzIz7e\nn+jo5t+KrL407u64ezjeRcTdu+222grhLC41Jk4I0fR8fd2ZNau/3Zh+/cLp0kW2dGoKPj7u9OwZ\nxNVXR3PFFZEuXcABaL286DZ1qsO4dgMGNEM2QogLSREnRBs0cGBYnQPt27XzYd68KwkIaLmTN0Tj\niho2DI8A2wslA0RfcQUhnTs3Y0ZCCJDuVCHaJH9/PQ8/3Ierr+7I4sV72LUrG4NBz4wZPRkyJJIO\nHXxccq0y4Ry+MTHc8OmnfHPnnbWWXWl/5ZUMnzsXr+Bgh2MFyzMzyU9JwVRSgkdAAAGJieiDguw+\nRghRNynihGijDAYdQ4aEM2BAGMXFJnQ6N9mTU9QpoGtXJq5aRd6hQ+QlJ6P19CSkWzf84uJwNxjs\nFv2WigpObNjAD7NnU3bBVmWG9u0ZOX8+oQMGoHGTjiEhGko+sYVo43Q6DYGBemenIVoAj9BQIkJD\niRg6tEGPO7V5M2vvvrvW8aLjx/n6llu4ccUKgnr2bKw0hWgz5KuPEEKIJlORm8uPTz1V53mLycS2\n//wHS0VFM2YlROsgRZwQQogmU5ieTtGJE3Zjjn73HSUOYoQQtUkRJ4QQosmYy8vrFyctcUI0mBRx\nQgghmoxnPWaf6nx90fu17O3shHAGKeKEEEI0Gb/YWDpebX/761733ot3dHQzZSRE6yGzU4UQNeTm\nVnDkSAHl5Zn4+roTH++Pv7/O2WmJFsrN05PL/v53Tu/YUWN5kXMCk5JIUhQnZCZEyydFnBACAJPJ\nypYtmTz22CZOnjy/aGtSUhAvvzyCvn1lGy5xcfwSEhj/5ZekLF/Orv/+F1NJCV7BwfR96CFiRo/G\nOyrK2SkK0SJpWsum3jZYMzIynJ2DyzEYDBQVFTk7DZcj9wV++imTW275GlsfCXq9lq+/vpHu3QOb\nPzEXI68V2woLrRQWluHhoSU01KPOuPLMTMwVFbh7e+MRGtqMGTqHvF5qk3tiW2RkJECDtsqRljgh\nBPn5Jp566kebBRyA0Wjm1Vd/Z+HCkXh4OB5KW1ZmJjW1kAMHzlBaWklsrB9JSYGEhXk2KK8TJ0o5\nePAMubnl+Pt70LlzIB06+ODmJluCuYoTJ0pZuzad+fO3k5tbRmCgJzNn9uG662Lp0MGnVrxnRIQT\nshSidZIiTghBWloBKSn5dmPWrEnjxIkS4uMNduMyM8t46aVf+fTT5BrHw8K8Wbx4NH36OO6WNRot\nrF9/glmzNlBcbKo+rtdrmTNnCDfdlCBbhLmAY8dKuP32VRw5UlB9LC+vnOef38J77+3jk0/G0rFj\n7UJOCNE4ZHaqEIKyMrPDGKsVyssr7caUl1v417+21SrgAE6fLuWWW74mObnQ4XNt357D3XevrVHA\nQVWL4FNP/cj69ccdXkM0LYsF/ve/PTUKuAsdO1bIwoU7qKxstUN2hHA6KeKEaEPMZitpacXs2pVL\ncnJBdfEWGFj3GKZzPD21GAz291hNTS1k2bKDdZ4vKTGxenVajWMajabG5uklJZX885+/2H2e5577\nmezsCiorrXY3XhdN59ixYpYu3W83ZtmyQxw7Vmw3pq049zqX16toTNIfIUQLUVpq5sSJYsrLzQQE\neNC+vXeD/iCkpRWzaNEuPvnkIJWVFgCGDYviiScGkZTkz4gR7dm0qe4Wrjvv7E779t52nyM5Oc9h\nHkuX7mPq1C4UFprYsSOLbduy8PXVMWJEezp1CiAnp4Jt2zLtXiMrq5QNG07w0Uf7iY/355ZbOtO5\nc6AshdKM8vLKMRrtt+BWVlo4c6acuDj7XfCtWVl+Prl79nD022/JO3yYoKQkOl59NX4JCbj7SFez\nuDRSxAnh4sxmK7t3n+Gf//yFn346CVS1ik2b1oOpU7vSvn3NPwRGo4WMjFKMRgv+/nrCwz1JTy/m\n5ptXcOpUSY3YH388yZYtX/LZZzcwZ84Qxo//koKC2tsftW9vYMqUbg6LxooKx92yQUGe7N6dy113\nraGs7Hz37IIFOxgwIJy//32Iw2sAnD5dwrZtmWzblsmyZYe48cZEnn12sN2ZkaLxeHjU78+Hh4e2\niTNxXca8PH597TV2vfVW9bHUVavY9sor9LrvPnrPnIk+IMCJGYqWTrpThXBxW7eeZvz45dUFHEB5\nuZk339zJ7bev5vjxUgAslqpi789/3sDQoR9z5ZXLuOaaz/j88yN88smhWgXcOZWVFh5//HtCQ734\n6qsJ3H13D/T6qj+8vr46HntsAKo6rl4D1Nu3d9zi8sADfZg6dXWNAu6c337LYt++XPz97RdiWq0G\nd/eaH1/Llx9m+fIU6a5qJu3b+9K7t/0lQpKSgujYse22wqWtWlWjgLvQrkWLOLpmTTNnJFobKeKE\ncGE5ORXMmrUBs9n24PCUlHzWrKkaY7Z162nGjVvON9+kVS8VkptbxtGjRbzzzm67z5OcnEdqagGJ\niX48++xl/PjjrWzefBubNt3Cww/3trlUhC2dOgUQFeVr53wge/fmYDJZ6ox5/fXt3H9/b7vPM2pU\nLN9+m17r+Lx52zh50naxKhqXweDOM88MwV7N/Pzzl+Pn1za7uMsyM/l17ly7Mb/OnUv56dPNlJFo\njaSIE8KFHT6cT0aG/YHh8+dv5+jREh544LvqsW4X0uncKC21P6sUqO5GdXOD6GhvevYMp107rwbl\nGxLiweLFo/Hzsz0B4q9/Hcjy5YftXuPkyWL69Alj6FDbq/jHxvozaFA7fvnlVK1zhYVGTp0qrXe+\nGo3m7OxJab27GH37hrJkyfWEhtZ8nQQFebJ48WgGDgxzUmbOV5KRQfmZM3ZjSk+fpuRU7dexEPUl\nY+KEcGGFhUaHMXl55Rw5UsDp07aLF7PZiqenlvJy++PVHM08ra/u3QNZuXIi3313lHff3UtZWSWX\nXdaOadO6ExPjb7PQ/KNjxwpZsGAkv/6axYIF2zl6tJDQUC8mTEhEo9Hwf/+3pc7H1qc3tbzcTHJy\nAatWpbJ16ymCgjy5/fau9OgR3OAFidsynU7DyJFRrF07iSNHisjPL8XPz4OEBH8iIhr2BaDNar27\nJolmIEWcEIDVasXNzQ2r1YorbUXn4+O4K8pg0FNYWHsywjkrVx5h/PhEu0t/xMT4ER/vf1E52hIf\nbyA+vju33tqJykorfn56dDoNZrOVUaNi+PDDAw4eH0BYmCdjx3ZkxIgoysrMmEwWbrttld0ZsCEh\nXna7c6Fqlu9HHx3i2Wd/qnF83bp0evQI4e23r601WUTYFx7uSUJCqGyldAGfdu3w8PenosD2OnoA\nnkFBeMsOFuISSHeqaNNKSirZuTOXZ5/9kWnT1vHCC7+xfXsORUUmxw9uBomJAYSE2G/RuP/+3nV2\nXwIcOJBL9+4hBAfbvo6bm4Z//WsEgYGN0xJ3IX9/PcHBHuh0Vc1jWq2GyZO72H1Mp06BdOp0fsae\nr687oaEeREZ68cADfew+dvbsQYSH229J2749u1YBd86ePTn87W+b67X4sRD2eEdG0v/RR+3GDHjs\nMbykiBOXQIo40Wbl5xv5z3+2M2bMF7z66jbWrElj4cIdjBu3nBde+JXc3Lpbt5pLeLgn//73FXbO\ne3PDDfEkJATg7V13w/rcub/w+utXMXZsXI3uxh49Qvj88/FcdlnzjV3q1i2Q+fNH2uz2jIz04e23\nR9VZUF5zTQcefLCvzXP339+L66/vaPe5y8rMLFy4w27M+vXHSE11vKuEEPZYrVbiJ0yg86232jzf\n9fbbiR07tpmzEq2NxpW6jhqZNSMjw9k5uByDwSBdHmd9+mkKs2ZtrPP8P/4xlOnTuzq9e9VotPDL\nL6d5+ukfq/c3dXPTMHZsPH/9a3/i4gxYrfDhh8nMnv29zWuEhnqxfPkEoqK8SU8vIj+/Ai8vHTEx\nBgwG28VfTk4l+fmleHq6ExnpjVsjfuUzmSwcOlTAmjVpbNx4HC8vd+64oyv9+oUTHW1/QeHSUjOp\nqYVs2nSclJQ84uMDGTGiPXFxBnx87I8QycgoY8CADxzm97//jeK66zrYPCfvIdvkvtjmZjRyevdu\nkpcvJz85mcCkJBJvvJGATp1wN7TN5VfktWJbZGQkNHCWlRRxbYy8eapkZ5czevQXZGbWvRxFQIAH\n3313c4NnaDaV/HwT6emFVFSYCQz0JCbGF73+fGVVUlLJ2rXHePbZnzhzprz6+BVXRPP880NJSKjf\nH4xjx0r44ovDLFq0i6IiI3q9lttu68KUKd3o1MmvUX8njUaD0WhBq9VcVJGo0WgaVGRnZJQxaNCH\nWCz2H/POO6MYPVqKuIaQ+2Lbufui0WiqJjE08DXbGslrxbaLKeJkYoNok06dKrVbwAHk51dw8mSx\nyxRxAQE6evcOBuDMGSM5ORXo9W6EhFQtjOvj487EiXEMHtyuutgLDfUiNtYPb+/6rZp//HgJf/rT\nKtLSzg/GNhrNvPvuXj7/PJnlyyfQuXPjTYCwWq3V4+Uu9vENERLiwahRMXzzTVqdMRpN1TImrsZS\nXk7R0aMYCwvR+fpi6NgRrbf9VkvhOqpfq228gBONS4o4IVqQkydL2bjxOK+++junTpUQHOzFX/7S\nh9GjY6oX5G3XzuuiCk+rFT766GCNAu5ChYVGnnvuZ95559p6F4WuRq934777etst4m6+OYnYWNfq\n5so/cIBfXnyRYxs2VB+LHDyYwc88Q1DPnk7M7Dyz2UJmZhkVFRZ8fNyrv1wIIZqOdKe2MdKMXeX0\n6XJGjfq8zrXVAPz89KxffzORka7R2nHiRCnTp69h377cWueionxR1XHExNhfXsPR9a+8cpnDhYHX\nrbuZbt1a7n6PRqOFb745ysyZ62vthDFyZAf+9a/hdovg5n4PFRw8yPLx4zEV1170WevhwYQvv3R6\nIXfkSBGff36Yt9/eRWlpJSEhXsya1Y9RozrW+f4x5uVRcPgwZw5WLX0T1LkzAZ06oWtle4nKZ25t\nck9sk+5UIeopLMyT2bMH8uijm+qMefTR/kRF+bjE+BWrFT7++KDNAg6qdjl45ZXf+c9/hl9092Rh\nobFeOzvk5ZU7jHFler0bY8Z0pFu3W/jllwy2bz9NcLAX11zTkcTEAAICXGebKIvRyLZ582wWcADm\nigq2PPcco5Yuxd1JXavJyYVMnPhVjddFTk4ZTz+9mU8+OcjixaOIiqqZW3FaGuvuu4/cvXtrHA/u\n3p1rFy3CNza2WXIXoqWTIk60CKWlZo4cKSA1tQCLBTp2NJCQ4H9J+zKOGtWRfft6sHjxnlrnbrkl\niRtvTHCJAg7gxIkS3nprl92Y5csPM3NmHxITL27ygaenlnNjr+2xt5RJS+Hu7kZCgoGEhCRuv70z\ncH7Mkik/n6Ljx7GYTHgFB+PdoUPVoHQnKDl+nNRVq+zGZGzdSnF6OgFduzZTVueVlpp59tmf6izs\n9+7N4YsvUnjwwV7V97c8K4vVU6fiFx1N1N13Y66o4Oj69RRnZJC7dy+rp07lhk8/xTM8vDl/FSFa\npJb/aSxavZMnS3n66Z9Yty69xvHevUNZsOAq4uIubvxSYKCexx/vx403JrB6dRr79+eSkBDADTfE\n06lTgEtt3J2fX+GwlcxisZKbW37RRVx0tA9jxsSxcmVqnTGxsf7ExjbuDFVnO1dcmMvLydqyhZ/m\nzCE/JQUAracnPaZNo9u0aXhH2d7LtSkZi4vrNRDe6KSuqbS0Qn744YTdmDfe2MGkSYnVXdQFaWl0\nv+MOjm3axOHly3H38iJ+3Dh8IiLYNm8eBUeOkLtvH1FSxAnhkBRxwqXl5Rl56KGNbNlSe3zjzp3Z\n3Hbbaj7//AYiIy9uBqnBoKNv3xCGD4+htLTU5bbdOkevr99EgguXHGn4c7jx0EP9+O67o3Xus/ri\ni8OaZGcHp7NaObp6Netnzqxx2Fxezs433+TkTz8xavFivNq1a9a09L6+aNzcsFrs7zer93NOYZ2b\n67hrvbDQSGGhkXbtvDCXlJC+ejW733mnRsyu//4XvZ8fQ55+ms1z5nD4yy+Jvuoql3wvNgaNRkPp\nyZOU5eai0WrxjY5G56R/Q9GyyY4NwqUlJ+fbLODOOXaskB07Tl/y82g0GiwWi8v+0Wjf3odBg+wX\nEB07+hETc2l/CLp2DeDzz8fTuXNQjeORkb588MEYLrusdbaOlBw/zvezZ9d5Pnv3bk5t2dKMGVXx\n7dCB+PHj7cZEDRuGISameRL6A09Px+0AGs35LyE5O3fWKuDOMRYW8vuCBXS97TYqS0qc1oXd1Mqz\nstj9xhuoV13F56NH89k11/D1TTdx6vvvMZe37PGmovlJS5xwWRqNhk2bjjmMW7JkH9dd17FRdxRw\nNd7e7jz11CBuvPGrOheq/cc/hhIUdOmtZL17B7N8+Q2kpRVz5kwpPj464uL8W/WSEXmHDuEdEoJH\nYCClWVmUZGbWitm+YAHtr7kGmnGVfY1OR78HH+TY+vUYC2tvBebu5cWQv/8drVf9WqIri4upLC5G\no9XiERp6yfnFxfkREeFjd83FMWPiiIryxlJezs5Fi+xer+j4cXwjIwmIj8fioPWxJarIzmbTo49y\nfGPNnWJy9+9n5Z/+xJWvvkr8xIlotC1zCR/R/Frxnz3RGhQUGB3GFBebai0V0Rr17h3C0qXXExJS\n8w+2n5+eN9+8hiFDGm8jbT8/HUOHduDKK6MYODCsVRdwxcUmjms6kjziedZGziRj3L+Ife5tggcN\nrRl38iTmsrJmz8+vUydu/OorEiZMQHPBN5WYUaO4ccUKArp1c3gN45kzHF+7lpWKwgcDB7JsxAh2\nzptH4dmxfxcrJMSDF18cVud5vV7LX/7SF73eDWNhIad+/dXhNStLS4kcPPiS8nJVp7dvr1XAXeiH\n2bMpOX68GTMSLZ20xAmXZbVa6dcvgvff32c3btiwKPR6N5ftCm0s7u4aRoyIZN26SRw+nE9+fgUG\ng47ExACXWQqlpcnJqWDu3N/46KMDtc49OP0eugYEk7n2KwB82rVD6+nZ3CkCVYXciFdfpf8jj2As\nKkLn7Y1vx464eTgurityc9n63HMkf/75+WP5+fz28svseustxn/++SXNbL3iikgWLbqGJ5/8scYs\n1ZgYP+bPv4ru3QMB0Gi1uHt61rlcyjk+kZH4xsVddD6uylJW5rAl0lxRQe6+ffg6qXtctDxSxAmX\n1rdvKB4eWioqbA+0BxgzJr5NFTDh4Z6Eh9dsdWtLv3991WdfVVVNtlnAAby2OI15f5+MbvN3mEpK\n6Pfgg04dfK7R6TDExzf4cZlbttQo4C5kLCzkuwceYPzy5Re9yK6np5Zx42IYMiSaAwdyKCkxERjo\nQUJCQI3ufY/gYLpNmcK2V16p+2IaDaE9etRocWwtKsvKKDx61GGcra58IeoiRZxwaTExBv73v1Hc\neec3NrtM//3vKxp9U3bRcpnLyylKSyPj55/JP3KEgLg4IocMwRAXV6sV7cSJEubP/93u9RZ8eIpn\nJ02haMdPtBsypClTbxKmwkK2zZtnNyYvOZn8lBRC+/e/pOeKiQkkONj+n5T4sWPZuWgRlaW2d0rp\netttrbIVDqqWq/GJiKA0K8tunFcjjFUUbYcUccKlaTRV3TWrVt3EsmUH+eKLw5jNFkaO7Mj06d3p\n2TMYD4/6f2s3mSwcPVrMiRPFaDRVMzo7dLj4raqE6zAVFrLvnXf47eWXa53r9/DDdL/nHvT+5ze2\nP3GimOJik91rpqYW4PPXUQx5YFqzLy/SGCqLiqq3tbLHUWHRWPySkrhh2TLW3HUXpadrzirvPHky\n/R59FG09uohbIq23N73vv59v77uvzhg3d3dC6jHGUYhzpIgTLk+r1dCjRyBduw7moYf6YrVaCQz0\naPD2UhkZpcyfv4OPPz5Q3arn4aHlvvt6MWNGHwICWl8XTltyfP16mwUcwO/z5uEfE0P8pEnVx+rb\nA+2fkIh3VMvcz1Pj7o67lxeVDiZkaPXNt/ZfcN++3LRmDXmHDlF47Bg6Ly+CunTBEBtb71m2LVX4\ngAGE9e7N6Z07bZ6/7Omn8e3QoZmzEi2ZFHGixdBqITT04r6l5+RUMHPmRrZurbnmXEWFmfnzt3Py\nZDH/+MflGAzylmiJKrKz2frCC3Zjtr74ItFXXFG9tEZkpC+ento6FzYGiI42EB7ecgsLj7Awuk2Z\nwq7//rfOGK1eT0BiYjNmBZ7h4bQLD6fltW1eGq+ICK556y12LVrEgQ8+wGysmn3vExHB4Geeof1V\nV6HRuc5OMcL1SdODaBP27TtTq4C70GefJZOSUtCMGYnGVJyRQcmpU3ZjSrOyKD55svrnDh28uffe\nXnYf88QTAwkObrndexqNhiRFwd3bu86Y/o88go+0/jQb76goBs+Zg7JhA+O/+IIbV6xg4po1xI4f\nj7uvDO0QDVOvZgdFUS4DBgP7VFVd94dzT6iq+lJTJPeH50kHCgALYFJVdWBTP6doHTQaDR98sN9h\n3MaNx+jbN0RmerZAjralshWn0WiYOrUbBw+eYe3a9Fqx99zTk5EjoxsrRafx79yZGz79lHUzZtQo\nYt10Ovo9/DCdb7/d5WaDmvLzKT+7JZVXeHjr62bVavGNjcU3NtbZmYgWzmERpyjKHcB84Efgr4qi\n7ABuUVX13GI/TwFNXsRRVbyNUFU1rxmeS7QiJpOFrKy6V5Q/5+RJ++tXifPKy82kpxexa1cOeXnl\nxMT40a1bMO3b+zglH5+ICDz8/akoqLs1VW8w4P2HTdXDwz35z3+u4J57erJs2UGOHSuiW7dgJkxI\nJCkpAF/f1tG9Hty7NxO/+Yb85GRKs7Nx9/AgIDER3w4d0Li7zu9ozM8n44cf+PXf/6YgNRWA6OHD\n6ffww4T07o1bM47dE6IlqM+790lgtKqqvyqK4gUsAjYqinKNqqr5QHNtcKdBun/FRdDp3OjVK5Tf\nf7c/A697d2mFq4/c3Apef30nb721u8ZxHx8db7xxNVdeGYVW27z7XnpHRtJv1ix+fu65OmP6PvQQ\nPtHRtf6NAwP1DB4czpAhEZjNVWMvW+PrwCM4mHAX3gnBVFDA7//+N3vfe6/G8RM//MCJH37gmjfe\noOPYsbIllRAXqE9RFKWq6q8AqqqWqao6FdgE/KAoSjjQXJ92VmCtoii/KYpyTzM9p2gFrFYrEybY\nH7it0cCQIZHNlFHLZbFYWbr0QK0CDqCkxMS0aWvYs+dMs+dltVqJv/FGEurYLD5u7Fg6TZpktziz\nWq24uVlbZQHXEpzZv79WAXehDbNmUXzM8V7KQrQl9WmJy1IUJVFV1cPnDqiq+ldFUUqp6mJtrqk0\nQ1RVzVQUJRT4VlGUA6qqbj53UlGUEcCIC3LE0IwbVbcUer2+Td6XPn10PPhgP157zfbiri+9dAXd\nuoXj5SUzw86x9Vo5eDCH117bXudjLBYrixbt4u23r8fbu3nvpcFgYOTLL9Nj6lT2LFlCwZEj+MfF\n0X3KFMJ69MA3ou5dLjSa+rccttX3kCOXcl8qKyrYv3Sp3Riz0ciZ3btp16NHg/69nE1eL7XJPamb\noihzLvhxk6qqm+zFaxx961QU5d9AsaqqtfopFEV5EnhBVdVm7eZUFOVZoEhVVTv7t2DNyKh7NmJb\nZTAYKCoqcnYaTlFYaOLnn08xd+5vJCdXtRb16xfOX/86gGHDOgJG5yboYmy9VjZuPMntt6+2+ziN\nBrZsuY327eueEdnkrFYsRmPVGKo//ME3l5VRlJ5O2enToNGg9/XFJyoKzz+Ml6tLW34P2XMp96Wy\nqIjlY8aQf+SI3bh+s2bR7/HHW1RraZt5vZjNlGVlYamsRGcwoA8MrDO0zdyTBoqMjIQGDlFz2BKn\nqupfARRFGa6q6g9/OPfPs7NGm5SiKN6Am6qqxYqi+ADXAnUPfhHCBj8/HaNHd2Dw4AhycioAiIjw\nwmgI3NgAACAASURBVMfHHYPBg6IiKeIcqax0/MfTagVLPWeLNhmNxubm8OWnT5P69ddYTSYOf/kl\n2Xv2oHFzo+M119Dz7rsJGzRIxlw5gZuHB57BweCgiPMOC2tRBVxbkX/gAPuXLOHAxx9jMZnw69CB\nAY89RtTw4dXrMoqm0ZBpSZ8rirIYeFpVVZOiKAHAf4E+wMdNkt154cByRVGsVOX84R+XOhGivvz9\n9fj7yyy3ixEZ6Xj2aadOgQQEuN7aahajkbSVK8ndv5+Dn3xSfdxqsZC+di1Hv/2WUW+9RfvRo2u1\n3omm5abX0/Puu8n89Ve7ceGXuL+raHw527ez4uabMZeXVx8rPHaM9Q8+SOzo0Qx96SU8pZBrMg0p\n4noB7wK/KYqyAJgDrKaqiGtSqqqmAb2b+nmEEPbFxflxxRXRfP/9iTpjHn10AP7+rje2sCgtDavF\nUqOAu5DVYuG7mTNRNmyQxW+dIKxvX4K7diV3v+01HXtMm4afrKvmUipyc/n2vvtqFHAXSluzhoQJ\nE4gZN66ZM2s76j2WTVXVDGDC2ce8BXyjquq9qqo6XoBLCNEqeHlpeeGFYXTs6Gfz/NSp3Rg61DU3\nUyrLzibj55/txlSWlZFdx76WrZHVaqX89GnKTp2isti56yR6tWvHqMWLib/hhhotoe5eXgx8/HH6\nPPwwWjs7TziL8cwZsrZu5cjnn5P+9dcUHDqEuaLC2Wk1i/zk5BoLSNvy+7x5mAoLmymjtqfeLXGK\novQGPgQOU7XA76uKonwM3H92vTghRBsQG+uLqo7jl19OsWjRLgoKKujWLYS77upB9+5BBAS4Zle1\nxs2NM4cOOYzLT0lphmycr+DgQQ59+in7ly7FVFpKaK9e9H/oIcIGDkQfENBoz2MuLaWyrAx3Ly+H\nRZhP+/aMmD+ffrNmUZyRgZubG36xsXi3b++SM1Lz9+9n7V13UXjh0icaDV1vu41+jz6KZ1iY85Jr\nBmU5OQ5jziQnU1lSgs7P9hc/cWka0p26HnhcVdV3ABRF2Qi8BuwB2jdBbkIIFxUd7U10dDzXXRdD\nRYUZX193dDrXXotbHxCAvh5/SDyDg5shG+fK2b6drxWFyrKy6mPZO3fyzbRpdJsyhf6zZ19yIVee\nlUXWtm3sWLiQ4pMnMbRvT58//5mw/v3tFjduej3+SUn4JyVd0vM3taIjR1gxaVLtXUKsVvZ/8AFW\ni4XBzz8PrXgpDXdPT4cxeoMBN53rDa9oLRryqTvgXAEHoKpqiaqqdwEPNH5aQoiWwNtbS2Cg3uUL\nOACfyEjixoxxGBfer18zZOM85dnZrLvnnhoF3IX2LVlC9va61wKsj7KMDNbNmMG6GTPI3rWLspwc\nTu/Ywdp77uG7++6jLDMTjUbjkq1r9XVs/Xq727wd+OgjitLTmy8hJwhITERrYxb4hXrNmIFHSEgz\nZdT2NGRMXGodx1c0XjpCCNE09AEBdBg5EkN03Zvad548GUMrHzyff+gQJZmZdmN2LFxI3p49ZGza\nxJk9ezCX1H/os9VqZd9775G1bVutc27u7oT36cOpn3/ml+efZ8vTT3Psm28odTCuytWY8vPZ8847\nDuPOHDjQqpdE8enQgUFPPFHneQ9//6oxjqLJuM7Ox0II0cQCunZl9LvvsvmZZzi1ZUv1cTd3d3pM\nn07P++/H3cfxMiotmaMCDiBnzx5SV61i+4IFAEQMGsTwF1/Ev3Pn/2/vzsOjKs82gN9nZjJZJwsk\nJISsBMKSgGwBARdQWQRlEfKCFaHKJxZp1dZWq7jVb7FoRVHbSlVasQIetSLIIiACFcoiO7JlgxAC\nIZB9ncnM+f5IiAmZLclklsz9uy6uiznnnZlnXg5nnnlXm8+tys3FMTMJjkqjwehXXsGxDz7Akffe\nazx+fMUK+IaEYPI//4muQ4a04pO4jslotNiS2ZShqsoJ0biOpFKh96xZUGk02Pvqq6hr8nnDU1Nx\nx1tvQZeU5MIIOz8mcUTktq53tzmyNSO0f39MXLkSpWfOoCI/H2ofH4QkJSEoPh6SpvPfEjX+/jbL\n+AQFNftCvrxvH9ZOn47p69cjuFcvq8+tunrV7JITAx5+GMc//BCl2S07dWpLS7H+/vsxY9Mm6Hr2\ntONTNCdJEkwGg9P+/XyCgxGVloaczZutlguOj3dKPK6kDQlBv4ceQtxdd6E0OxvG2lr4R0QgpFcv\nTmZwgs5/xyIij1NQUIPjx69Blk+jrEyPMWNiMWZMLHr1CoZG0/5xVJqAAHQdPBhdB3f4MpduxVhV\nhYDwcEgqFRQru2r0mjIFOZs2NTumLyvDWVnG0GeftTqWTWUukZIkBHbvbnVbLUNFBS5+/z36tiKJ\nMxkMKD17Fue/+QYXdu6ET2Ag+s+Zg4hBg+Bfv4VRh1D5+CD14YetJnEB3bohrE8fjx73ZzdJQmBc\nHNdXdAH3H41MRF7l/PlKzJq1HvPmbcSGDdn497/z8N///R+MG/cZNm48D4PBxVt6eShjTQ1Of/IJ\n9r76KvrOnm2xnG9ICHQ9eqA8r+WCzsc+/BA1Nrpjg2JjoYttvmBBUHS02Ra4G51eswYmO9dYM+n1\nyPnqK3w+YQIOvPEGLv/wAy7s3IlvHnkE62bMQLkd79ce4TfdhKFPPmn2nCYgABNXrOj0S4yQ6zGJ\nIyK3UVZmwK9+9S0yMlouPWkyKXjssa04caLYBZF5vrKMDOx5+WVcPnAAkkqFlLlzW7SahSYlYeTz\nz+PA0qVmX8NYU2NzIVvfLl0w+uWXmx1TqdUw1dXZjFGpq6vffNcORSdOYPsTT5gtX5abi20LF8Jg\nZfZoe2mCgjBg4ULcK8uIHTsWWp0O/uHhGPbUU5ixYYPXtfKSa7A7lYjcRlZWGQ4eLLB4XlGATz45\nhQEDRjukW9WZ9EVFqKuqgkqrdXoLjSRJyPnmm8bHJ//5T3QbPBg3P/ssTEYjFJMJoT17Im/3bvz7\nhRcsbqPkHx4OHzsmfnS/9VbctmQJdr/wAox6PSry8xFqRzdpz3vugdrf3+YYSMVgwMmPP7Za5uqJ\nEyjNyEB4B+636hMUhKjRozF+6FDoy8ogqdXw9YJ1Bsl9MIkjIreRnW275WTjxmw880waIiKsr0/l\nLqovXULu9u04+OabqLx0CVqdDoMWLkTSlCkIctZyJoqCS3v3Njt05fBhXDl8uPFx6rx5yNu1y2IC\nBwBDn3wSvnZsZq4JDETy/fcjevRoFJ08iaorVxCekgL/8HCLq/yrNBrEjxtn1yQWfWkpzm3ZYrNc\n6blzHZrEXafy84OfHQvfEjkau1OJyKNIUrOtNd1adX4+tjzyCHY9/TQqL10CAOjLy7H/tdewdto0\nlGVkOCcQSUKAjda/M59/jpGLF0NtIRmJGDgQCRMm2P+WajV0iYmInzwZ/R56CBHDh2PyJ5/ANySk\nRVmVRoMJH35o/y4NkgRJZfvryysmFZBXYxJHRB3CUFKCa0eP4sq+fSjLyIBiMNh8TlJSyy/4G02Z\n0gthYe7fCidJEjLXrm3W2tVU9dWr2P3SS1ZbvhxFURSrkxkAwFBZCf/ISNy3fj2SZ8xoTJJ8Q0Mx\n8oUXMP7DD9s94zMsNRX3bdyIsUuXIiotrb5Ld/FizNyyBT3uuMOuxAwAfMPCkDxjhs1yoTaWQ6GO\n4em7cXgSdqcSdbCOWOvMnZn0elzZvx//fv55lDS0NEkqFZKmTkXaU09Z7ULs1SsEo0ZFY8+efLPn\nVSoJ99/fF2p1h4TuUFWXLjUulmtJ3s6dKM/ORmj//h0eT5f+/RGZloaCAwfMno8dOxbBPXtCGxqK\n2954A8OeegpGvR4+Oh0Cund32PUblJCAXgkJSJoxA1AUqLTa1r+2SoXkmTNxfMUKKEaj2SIxt91m\nc007chzFaER5Tg4u79+PywcOwC80FPHjxyOsb19ow8JcHV6nJXXiLxYlP9/8F4E30+l0KC8vd3UY\nbqcj6iU3txKHDhVgy5bz0GgkTJrUEwMHhiM6OsCh79NR2lonedu2YdO8eWbPBXbvjimff46ghASL\nz8/NrcSCBVtw/HjzsVNqtYT335+AO++MccmkBkNJCUoyMlBVUABJrUZor17QJSRAsrC5d+np05Dv\nvNPm696zZg2633qro8M1q+riRez7v/9D5ldfNc7qlFQq9J09G0N/8xv4d+/e5td29r1FMRpxadcu\nbH74YRj1+mbnIocNw13vvouAG5Y6cQVvuOcqdXW4sG0btj76aItZyNE334yxb7+NgB49Go95Q520\nRXR9S3erbm5M4rwM//OY5+h6OXToKn72sw0oL2/+5dKtWwBWr74Hffva7jZ0tbbUSU1BAT4fP97i\n4HUAGP7MMxj0xBNWW18KC2tx+nQx1q/PRGmpHrfc0gMjR0YjMTEIarXzE7jSM2ew9Re/QPHZs43H\nJJUKA+bPx02LFsHPzGD/ipwcrL71VptLZkz78ktEDB8OkwnIza3A5ctVUKslxMYGISrK9u4KrWXS\n61GenY2yCxcgAQhOSLCajNrLJfcWRUF5Tg4KDh7EpX374BscjPhx4xDWpw+0Xbo4NxYLvOGee+3I\nEfzrnnssXuuJEydi7DvvQB1Q/wPWG+qkLZjENcckzgz+5zHPkfWSk1OOiRO/QEWF+TFgUVGB2LBh\neod8QTtSW+rk8u7dWC+E1TJanQ6zdu6EX2Skzddzh67oipwcfDllCmqKisyeT5k3DyNefLHFhABT\nbS2+XbgQ55os7XGjgMhIzPjmGxQZAvG3vx3HRx/9CL2+vnuwa1d/LF58M+6+Ox7Bwe1LsJzB1fcW\nd7hWzHF1vXQ0k8GA7595Bmc+/dRquZlbtiAsJQVA56+TtmpLEseJDUQOtmfPJYsJHABcvlyJEyeu\nOTEi5zFUVNgsoy8vt3swv6IoLv9Szt2+3WICBwA/fvQRynNyWhxX+fpi6JNPmt+GqsGt//M/KFN0\neOyxbXj//WONCRwAXLtWjd/85jv84x8noddzlwpb3OFa8Ub64mJkrVtns5w9O3ZQ6zGJI3Igkwn4\n4ouzNst9992FTjl7S2vHhtd+YWHQBHjGuEBDWRmOf/ihzXJFp06ZPR6Wmop7ZRlBTcYDAfX1dOe7\n7yJ6zBgcPlyIAwcsL3D8+usHcO4cWy3ITSmK1X14m5Yjx+PsVCIHUhT7unM6a4tBaO/eCIqORoWV\noQwDH3kExadPQ1ddjcDYWLde9M1kMNjVumipjKRSoduIEbhv40aUZGSgprgYPoGBCO3dG4E9eqC2\n1oj33z9qPQaTgsOHryA52f3HUZL30YaFIf6uu5C9YYPVcsHx8U6KyLuwJY7IgdRqYPr03jbLjRkT\n1ykTOd/wcIx9802L632FJCRAUqmwfvZsyHfeiXNffw3TDTML3YmPToduQ4bYLKeLi7N63jc8HJEj\nRyJ+0iRE3347AqKjoSgKamqMyM+vtPn6ly7ZLkPkCiqtFgMfecRqme4jRiA4KclJEXkXJnFEDjZ6\ndA/4+1tu5A4P98eAAZ13f8XIkSMxbe1aRI8c2XhM7euLvrNmIWXuXBz4058AAHVVVdj6i1+g8Icf\nXBWqTSqtFgP/67+slvHv2hVd+vZt0+v7+6vRs6ftFra4ONvd1ESu0nXgQIx5/XWz50J798bYN9+E\nJijIyVF5B85O9TKcFWSeo+tl374reOCBDaiubr5mUliYHz799F6kpIQ67L06SnvrxFhVhdLMTFz6\nz39grK1F5rp1uGZm7FjkkCGYtHq1297kDeXlOLJsGY789a8tzqn9/HDv6tWIGD68za//3Xf5mDPH\ncleURqPC9u0CSUm6Nr+HM/DeYp631ItJr0dpRgbObd6MvO+/h29wMPrPmYPwgQNbzET3ljppLS4x\n0hyTODP4n8e8jqiXnJwK7Nt3CevXZ0GjUeG++3pjyJBIxMZ6xqB+R9RJ4Q8/YO3UqTbLie3b7d83\n0wUMZWUoPHQIh999F5cPHIDG3x/9HngAyTNnIrRfv3a99rVrtXj22e+xYYP52XuvvXY7Zs3q7ZIF\njluD9xbzvK1eJEmCYjRCUqstDhnxtjqxV1uSOE5sIOogiYlBSEzsjZ/9rD45Mdkzg8sFDGVlqKuo\ngKRWw7dbN4fOmjXZsV8qgBarvLsbn+BgRI8Zg8jhw4GaGhjq6uAbEeGQuura1Rf/+7+3YMSI7njr\nrYMoKqpffqVv3y5YvHgkRo6MdPsEjug6RVEAlapTjvl1R0ziiDqYuyZvtdeu4fLevfhh6VIUnT4N\nTUAAUn/+cyTPnOmwVrGAbt2g0misJmm+ISHwdZPV9W1RBwRAFxnp8FaEiAhfzJ/fH5MnJ+Lq1Rqo\n1RJ69Aj0iEV+ich1OLGByA3V1BiRmVmGEyeKceFCpcOXWKq9dg3/efllbFmwAEWnTwOon2hw5C9/\nwZf33ouio0cd8ks6KD4efWzs4DDk8ccRWN+N4PWiovyRmhqGfv1CmcARkU1siSNyIyaTguPHi7Fk\nyT7s3JkHAPD312D+/AGYM6cfYmMDHfI+Bfv3I+Nf/zJ7zlBZiS0LFmD2t98C7ZxsIGk0GPz447h8\n8CCKz5xpcT7mttuQNG2a3QmjXm9CTk45cnJKYTQqiI3VISkpBIGB6nbFSc6lGAwoP38e+tJSaAIC\nEBQXB02g/dd2TUEBys6dg1GvR0BEBHSJiVD5+nZgxETuiUkckRvZv78Qs2atR13dT12w1dV1ePfd\nw/jmmxx8/PGkdidydeXlOLhsmdUy5Xl5uHryJMLbMevyusDYWEz+5z9xae9eHH73XVQWFCA4IQFD\nFi1Ct2HD4Netm12vc/lyNd544yBWrz7VrGXy5pu74403xiAhwT1nt1Jz5VlZOPTWW8hYu7Zxpf+o\nESMw6oUX0OWmmyyuMQgAdZWVuLB1K3a/9BKqr15tPJ4wYQJGvvACghITOzx+InfC2alehrOCzHOH\nerl2rRaTJn2JvDzLcbz00igsWJDSrvepvnwZn6Sl2dwqZ8Ly5Yi7557Gx4oC5OVVoqioBlqtGjEx\nQdDpWvc7sK68HMbaWmgCAqBuxdZbZWUGPPXUTmzc2HKPUgDo2TMEsnwvunf3b1U8beEO14o7sqde\nyrOy8NV99zVLwK5TaTSY8vnniEhLM/9kRcHZ1aux83e/M3s6MDoaU7/4AoE2Fl52Nl4vLbFOzGvL\n7FSOiSNyE5mZpVYTOAB4++1DuHLFvs3jLVGp1fCxo5tU7efX+PeLF6vw2msHcccdMiZN+hfuuusz\nzJr1NfbsKWjV5uwanQ6+4eGtSuAAICurzGICBwDZ2aU4dOhKq16TnEsxmXDq44/NJnBA/QzlnU8/\nDX1pqdnzlbm52P3iixZfvzI/H+e3bnVIrESegkkckZsoLa21Waa4uKbFAsKt5RsRYXMXApWPD7o2\nzFC9dKka//VfW/D224dQVfXTex89Woj09HX49tu8dsVjj++/v2izzN//fgJ1dZ22Z8HjVeXn48TK\nlVbLFJ89i7KsLPPnMjJQV11t9fmH//xn1BYVtTlGIk/DJI7ITQQG2p6NGBTkA1/f9g9lTZoyBVqd\n5R0Ahv361wjrXb8H7PffX8SxY4UWy/7mN9/h4sWqdsdkiSRJKC623fpYWloLg8E9l3Oh+vFsxlrb\nP1T0FrrZDJW294+tvnoVihvvxUvkaEziiNxEr16hCA+3Pqbr0UdvQlSUn9Uy9gju3RtTPv8cITds\nSq3WajHi979Hv7lzofHxQWmpAW+9dcjqa5WV6XH2bEm7Y7JEURSkpobbLJeW1h3+/pyl6q40gYFQ\n2zGD1NKPC7+wMJvPDUlMhKaVXfVEnoyzU4ncRGSkH15//XY89NBms+fDw/0xfXpvh71fWGoqpn31\nFUozM1F15QrUWi1Ce/VCYHx84wzBmhojLl60PQDZnq7g9hg8uBu0WjX0eqPFMjNnOq5uyPECevRA\n6ty5OPr++xbLdElORvANPyyuC01Ohl+XLqix0l069MknoQkObnesRJ6CLXFEbmTMmB5YteoeJCaG\nNB6TJODuuxPxr39NRWKiY5fR0IaFISItDfGTJyNm3DgEJSY2W+JBq1UhMtL2kibBwVqHxnWj+PhA\nLF8+HiqV+Ylbzz03Av362W6pIdeRJAn9HnwQ/uHmW1VVGg1ue+01aENCzJ73j4rCXe++C0ltvrU1\neuRIRI8a5bB4iTwBlxjxMpzabZ671UtRkR7nzpWhttaILl38kJCgg6+vc39zXa+TTz45g6ef3mWx\nXFCQD779Nh0xMY5ZiNiSujoTfvyxGCtWnMDatZkwGk245ZYeWLRoCIYMCUdgoHM6FtztWnEX9tZL\neVYWDi1bhowvv2xc5qb7iBEYacc6cYrRiKJjx/DD0qXI3b4dQH0365DHH0fSlCnwi4pyzIdxIF4v\nLbFOzGvLEiNM4rwM//OYx3pp6Xqd5OVV4YEHNiAz0/y4t3feuRP33dfTaXEZDAquXauBogChoVqn\nj4PjtWJea+pFMRhQkZuL2pKS+h0b4uNbNZbNWFODqvx8mPR6aEND4e+Gydt1vF5aYp2Y15YkjmPi\niMiqmJgAfPzxJPz5z0ewZs3pxt0kEhKC8corozF6dHenxuPjIyEqquMX9aWOI/n4QJeUBMvzo61T\n+/lB19N5PxyI3BWTOCKyKS4uEP/3f6Pw6KMDcfVqNbRaNeLidOjSpWPHwhERkWVM4ojILmq1hJ49\ndejZs63tJ0RE5EicnUpE5CDGykrUlZejE481JiI3wpY4IqJ2Ks/KwoWdO3Hqk09gMhiQMH48ek2d\nitC+fSH52N6Jg4ioLZjEERG1w7XDh7F+9mwYKioajx35619x5L33cNe77yJh8mQmckTUIdidSkTU\nRlX5+dj44IPNErhGioJtv/wlSk6fdn5gROQVPKYlTggxEcBbqE88P5RleYmLQyIiL3ftxAnUFBdb\nLqAoyNqwAcMGDHBeUETkNTyiJU4IoQLwLoAJAFIA3C+E6OvaqIios6irU1Bba4Ik2b/OpiRJuHLk\niM1y57duhbGqqj3hERGZ5SktccMBZMiyfB4AhBBrAEwFwH4KImqz8+crsHfvZXzyyUno9SZMmJCA\nCRMS0KdPCNRq6wmdoijQ+PrafA+1j4/F/T6JiNrDU5K4HgAuNHmch/rEjoioTX78sQRCrENJSW3j\nsePHC7F06Q9YvnwcJkyIs5nIdb/5Zpvv0+/BB6GyI9kjImotj+hOhfm9xLgQExG1yeXL1XjwwQ3N\nErjrTCYFjz66FadPm98rtqnQ5GREDhli8bxvSAh6jBrVrliJiCzxlJa4PABxTR7HAGi2u70QYgyA\nMdcfy7IMnY4ry99Iq9WyXsxgvbTUWetEURScOXMZBQWWx6mZTAo2bsxBWloM1Ormv3Wb1osSFIQJ\ny5fjm4ULUfDDD83KBXTrhntXrULUgAGtGmvnqTrr9dJerJeWWCeWCSFebvJwhyzLO6yVlzxhZXEh\nhBrAGQB3ArgEYD+A+2VZPmXlaUp+fr6V095Jp9OhvLzc1WG4HdZLS525TpYuPYw33vjBapnk5DCs\nXz8NQUHNf+uaqxdDSQlKMjJQcPAgjHo9IgYMQFi/fvCPinJ47O6qM18v7cF6aYl1Yl50dDRgvufR\nIo9oiZNl2SiE+CWALfhpiRFrCRwRkUVare2JBmq1CiqVffdTn9BQRKSlISItrb2heSRJklCUlYWi\nzEyYjEYERkVBl5DARY6JOphHJHEAIMvyZgB9XB0HEXm+tDTbLWT3398XAQGcVWqLvqQE2WvXYt8f\n/wh9Q+uKpFKh9/TpSHv6aQTExLg4QqLOy1MmNhAROUxycigGDoyweD4w0Ae33x7rxIg8k0mvx4kP\nPsC/Fy9uTOAAQDGZcPaLL7Dp5z9H9aVLLoyQqHNjEkdEnV5hYS0yM8tw/nwl9HoTwsK0eO+9u5CS\n0rVZOY1GhWHDIrFu3X3o1YsDr22pOHcOB996y+L5olOnWkz4ICLH8ZjuVCKi1rpypQZbtpzH0qU/\noKCgCpIE3HtvEhYuHITU1DCsXj0ZZ8+WYM+eixjRR40I4yUU7v4OhX/bAb+xYxExaBACY9kiZ0nh\nsWOAjclxR997D7F33QW1v7+ToiLyHkziiKhTunKlBk89tRPbt+c2HlMUYN26LGzcmINVq+7B6NGR\nGDkyEqnhZfj6gQdw6uLFxrKnP/0UWp0O96xeja6DB7viI7i9qsJCu8qYamuZxBF1AHanElGnI0kS\ndu++1CyBa6quzoRFi7aioKAGNVeu4Os5c1DRJIG7Tl9ejvWzZ6M8O7ujQ/ZIwXFxNsuEJSdDHRDg\nhGiIvA+TOCLySJIkoa5OadGbV1lZh1278vHOO4esPr+wsBoZGcUo+vFHVOTlWSxnqKhA/p49jgi5\n0+mamgq1n5/VMgMfeQQqrdZJERF5FyZxRORRjEYFp0+X4J13jmLGjK8xa9ZGrF2bg7y8SkiShM2b\nc3HgQAGysmxvm1Vba0Lezp02y5397DModXWOCL9TCYyNxR1vvmnxfO/p0xE+YIATIyLyLhwTR0Qe\no67OhK1b87BgwRaYTD81we3efRHdugVg1ap78MIL30OIPujSxQ9XrljeWgsA/PzUMNmxa41iMrU7\n9s5IUqkQN3Eipn7xBQ68/jry9+4FAAR274603/4WcePGQduli4ujJOq8mMQRkcc4fbq0RQJ33ZUr\nVfj++4soLa3Fhg3ZmD69N5YvP2rxtfz81IiNDYI0ejSOf/CB1fftNXUqJA1vl+aotFp0u/lmTP3s\nMxTl5ECpq4Nf167wDQ93dWhEnR7vSkTkERRFwVdfZZpN4K6rqanv8szPr0BERAC6dQuw2Bq3ePFI\nxMQEolaTCv/wcFRfvWq2nFqrRcztt7f/A3Ry/iEhCE5KcnUYRF6FY+KIyCOUl9dh48Ycq2Wa7om6\ndOkBPPVUGkaM6N6sTHCwFkuW3I709F5QqST4R0fjnlWr4Bsa2uL11L6+mPTxxwju3dsxH4Ja58GW\nYAAAGaRJREFUMNXWouL8eZRnZaG2qMjV4RB5FLbEEZHHUNn42XnmTBFSUrrixx+voaqqDs89twsT\nJiTixRdHQa83QqWSkJoajjFjoqE0GQsXmpKCGZs2oeDgQZz59FOYDAb0vPdexNxyC3S9enXwp/JO\nSl0dio4dw8Fly3B+2zYAgC4mBmm/+x1ixo6Fb9euNl6BiCTFjkG9HkrJz893dQxuR6fTobzJHodU\nj/XSkrvViSRJWLbsKJYs2WexjK+vGmvW3Iu5czeivFzf4vzw4VH461/vQlSU5YVnJdR33UKSzJ53\nt3qxl1JXB8VkgtrXFx1x329tveRt24bNDz1kdtJIr+nTMeqVV+DbCSZFeOr10pFYJ+ZFR0cD9bcg\nu7E7lYg8gqIomDAhHr6+aotl+vbtguTkUKxbNx2/+MVN8POrLxsVFYjXXrvNZgIHAApgMYHzRJW5\nucj87DN8PXMm1k2bhiNvvYWSU6egGI0ui6kqLw/bFi2yOOs388svcfXIESdHReR52BLnZfgLyDzW\nS0vuWid7917Bgw9uQFVV83Xb+vbtghUrJiI+PhBAfdJ3+XIN9HoTgoI06NrV1yHv7671Yk7JyZNY\nLwRqioubHZdUKoz/298QO348JLXlpLg1WlMvedu2YdO8eVbLRI8ahYkff2xzMWF350nXi7OwTsxr\nS0scx8QRkUe5+eZu+PZbgcOHr2DPnnz4+2swblw8+vQJQ3j4T4maJEno3t179+usKSjAhjlzWiRw\nQP26d1sWLMCMzZsRlpLi9NjMbXF2o+KzZ1FXWenxSRxRR2ISR0QeJy4uEHFxiZg2rScAdMgYrxsZ\nq6tRceECSvR6qAMCEBQX59ZrxxWdOoWqggKL5xWTCdlff42h/fs7vfvYLyzMrjJqX8e0nrotoxG1\nJSWAJEEbFgapE3Xjk3O47x2IiMgGpwwHURQUHT+Ofa++irxduwAAklqNPjNnYtAvfwldz54dH0Mb\nXDl82GaZnE2bcNOiRdAEBTkhop906dcPkkpldSeMQQsXOj0uZ1EMBhSfPInTa9Yge9MmSJKE3tOm\nofeMGQjt189hXdzU+XFiAxGRFdeOHMGXU6Y0JnAAoBiNOP3pp/jqvvtQnp3twugsU/n42CwjaTSQ\nbK3b0gGC4uMx9Ne/tng+OD4e0aNHO+4NjUaYamsd93rtYKqrw/nNm/HF5Mn4ceVKVBcWourKFRz9\n29/wxaRJyN+xg9u8kd2YxBERWWAoK8POp5+GyWAwe766sBCnVq50yy/dqLQ0m2X6zZ4NdUCAE6Jp\nTqXVIuXhhzH6lVfgc0NrW/y4cZi8ahUCYmLa/T7VBQW48M032PTgg1g3dSr+8/zzuHroEIxV1vfU\n7UjlWVnY9thjgJlWZMVoxOb581GRY31Ra6Lr2J1KRGRBWXY2rp08abXMiZUrkTJ/PgJjY50UlX1C\ne/dG+IABuHr8uNnzmoAAxIwZ49ygmtCGhqL//PmInzABZTk5MNXVITAqCsGJiVA5YDJDZW4uNj/8\nMIpOnWo8Vnj8OE78/e8Y/swzSJk/H5rAwHa/T2td+O47q0m/yWDApX37oOMWZmQHtsQREVmgLyuz\nWcZYW4u6ykonRNM62i5dMH75cnTp37/lueBg3LtmDYLdYDeKwJgYdL/1VvQYOxah/fo5JIEz1tRg\n94svNkvgmtq/ZAmuHDhg8fmSJAFGo8MnGkgAcrdvt1kuf88eTnIgu7AljojIghu7+sxR+fhA44Iu\nSXsExsfjnjVrUHLmDC7s3AljbS26Dx+OrgMHItAB3ZXuqjw7G+e3brVa5uCyZYhMS4O6SWtcTWEh\nrh0/jlOrVqH66lV0Hz4cPSdPRkifPg5Z6kRSqey6puwpQwQwiSMisiikZ0+EJSej+OxZi2X6PfAA\nAnv0cGJUrePbtSsiR41CVMNEgU68wHuj8gsXbJa5vH8/aouLEdCQxFVduIAtCxag8Nixn8ocOIDD\nf/4zRr30EvrMmdPuZN1kMqHf7Nk49803Vsv1nDzZK/6dqP3YnUpEZIFPaChuX7LE4pIPvqGhSH3o\nIcADloRQFMV7EgN7ZtxKUuP6eKaaGuz5wx+aJXBN7fnDH1B48KBDQgsfOBAhCQkWz3dNSUGXvn0d\n8l7U+TGJIyKyInzoUEz78ktEDhny00FJQuLdd2Pa2rVuMa6MmgtJSLC5dErixInwCw8HUD+BJWfT\nJqvlD739tkNmtfpFRWHSP/+J8AEDWpyLGj4cEz74AL4REe1+H/IO7E4lIrJCUqsRPnQoJq1ejfLz\n56HU1kIdFARdQgJUWq2rwyMzdAkJSJk7Fyf+8Q/zBSQJgxYuhKphRwh7ul/z9+yp7351wPjHoMTE\n+rGKmZkoyciApFIhLDkZwUlJ8AkObvfrk/dgEkdEZAdNUBDCUlK4ebcHkHx8MPhXv0L11avI+vrr\nZudUGg3ufOcddBk4sMkTnD8T1Cc0FBHDhiFi2DCnvzd1HkziiIio0/GLisKtr7+OgY8+iou7dqH6\n2jWEp6YictgwBCUkNBvneL371dr6bQnjxzd2vxK5CyZxRETUKfkEByN8yBCEDxkCSZIsTuzQJSai\nz6xZOL16tcXXGvTYY43dr0TughMbiIio07M2M1fy8cGw3/4WcXfe2fKcSoU733kHXW+6qSPDI2oT\ntsQREZHX84+Kwh1vv42SjAyc37oV1VevImLQIESPHAldYiIkDb8uyf3wqiQiIkLDZIO0NHQbPhyA\ndyyMTJ6NSRwREVETTN7IU3BMHBEREZEHYkscERG1ib6oCOUXLkAxmWCIjoZPZKSrQyLyKkziiIjI\nKkmSGpfoUBQFdZWVyN+1C/955RWU5eYCAHyCgjBo4UL0nT0bflFRLo6YyDswiSMiIrP0paUoOX0a\nWevXoyw3FxEDByJh3DiUnT+PrQsXNitrqKjAgddfx6V9+zD27bfhx/0/iTockzgiImqh5soV7H7h\nBWQ32bYq99tvcfDNN5Eybx56TpqE7I0bWzwvb9cuXD16FDF33eXMcIm8Eic2EBFRM4qi4OQ//tEs\ngWvqx48+QtTQofAJDDR7/ujy5TDV1nZkiEQEJnFERHSDytxcHFm+3GqZk6tWIXnGDLPnynNzUVdd\n3RGhOY2+uBhlGRkoy8xEXXm5q8MhMovdqURE1ExFXh6MNTVWy5RkZaFPerrZc7rYWGj8/Zsdq6us\nRPm5czBUVsI3OBhBCQlQ+/k5LGZHMZSWIv/f/8a+JUtQmp0NAIi46SYMf/ppRA4fDnVAgIsjJPoJ\nkzgiInKogQsW/LRZvKKg6Ngx7H75ZVzev7+xTNzYsRixeDFC+/VzUZQt1VVU4PDbb+Poe+81O154\n9Cg2PPAAbv3f/0Xyz34GlVbrogiJmmN3KhERNRMUE2OzlSw0KQkV+fktjve45RZEDB7c+Pja0aNY\nO21aswQOAHK/+w5rp01D6enTjgnaAUrOnGmRwDX17+efR3lOjhMjIrKOSRwRETUTGBeHQb/4hdUy\nQ594Ahf37Gl8rAkIwNBf/xpjly1rXF6krrISu198EUa93uxrGCoqcGjZMigGg+OCbyNJknD2s8+s\nF1IU5P/nP84JiMgO7E4lIo8nSRL0xcUwGY3w0enY3dVOkiSh/7x5KM7MNDtDddhTTyF2/Hj0GDMG\nFXl5UOrqEBwdDW1UFCBJjeXKz51DwcGDVt8r6+uvMey3v4UuKcnhn6M1THo9Ck+csFnu2smTjQsf\nE7kakzgi8mhlmZk4v2ULfvzoI9RVV6P7iBFInT8fXQcMgMbCEhhkm1+3brh1yRIMnD8fmevXo+z8\neXS76SbEjxuHkN69oW6YuODbtSsAQKfTofyGWZwGO2Z1KiYTDJWVjv8AraTy8UGgHTtN6KKjmcCR\n23D7JE4I8RKARwBcaTj0nCzLm10YEhG5ieLjx7EuPR36JslC9saNyN64ESOeeQb9589nItcO2tBQ\nRAwfjm4jRjTbdsvu5wcH2ywjqdXQ6nTtCdMhFAD958xBzqZNVsvFjBnjlHiI7OH2SVyDpbIsL3V1\nEETkPmoLC7H54YebJXBN7VuyBJFpaYgcOdLJkXU+rU3ertMlJCB69Gjk795tsUzyjBkIjIlpT3gO\n0yU11Wq8fWfPRnCvXk6OisgyT5nYINkuQkTepPjsWbOzI5s6sWIFTBYG1VPHUwcEYNSLL7ZYM+46\n39BQDHrsMUg+Pk6OzDy/8HDcsWwZUufNg0rzUxuHxt8fab/7HYY/+yx8goJcGCFRc57SErdICPEg\ngB8APCXLcqmrAyIi1yo7f95mmfy9e2EoL28ct0XOF5aaiunr1uHAn/6Ec1u2AIoCSaVC7+nTMfhX\nv0Jw796uDrEZ/+7dcfN//zdS589HRX4+JEmCLi4OgbGxzSZtuA2TCZUXLqCmpAQaX18ExsZyCIEX\ncYskTgixFUBkk0MS6ocoLAbwFwCvyLKsCCH+B8BSAPOdHyURuRONHav9a/z9Iak8pcOh8wrt3x93\n/vWvqMjNhaGqCtqgIATFxblNC9yNJLUauqQkl8+YtaUyNxc/rliBEytXwtiwV23UiBEY+dxz6Dp4\nMCS12sURUkdziyROluVxdhZ9H8B6cyeEEGMAjGnymtC5wWBZd6PValkvZrBeWnL3OolISbFZJvXn\nP0eX2FhIDmxBcfd6cRWb9aLTISQ83HkBuYmOul6unT2LDXPmoDQrq9nxy/v2Ye306Zjy6afoOX68\nQ699R+H/IcuEEC83ebhDluUd1sq7RRJnjRAiSpblyw0P7wNgdiGfhg+6o8mhl26c7k7mlwEg1os5\n7l4nAXFxSE5Pt7hAq1anQ/y4caioqHDo+7p7vbgK68W8jqqXs+vWtUjgrlNMJmx7/HHM2LQJvg0L\nL7sTXivm6XQ6yLL8cmue4/ZJHIDXhBCDAJgAnAPwqGvDISJ3oPb3x4jf/x4AWiRygVFRmLhihduN\ntyJyhNrCQhx+5x2rZSovXUJJZiYi3TCJI8dx+yROluW5ro6BiNyTX1QUbnn1VQx85BEUnz6Nuupq\nBCckILRPn8atn4g6m7rqatQUF9ssV1vKOYCdndsncURE1qj9/RGWkoIwO8bIORq3XyJXUPv5QavT\nWVwj8Tp3WESZOhaTOCKiVtBXVqLk1Clc2rcPpTk5CElMRPcRI6BLTITajhmzRO3lHxmJwYsWYd8f\n/2i5TEQEQrkwcafHJI6IyE6GsjIc+8c/sG/Jkhbnhj/9NPo/9BB87Nhqiqg9FEVB0pQpOLFyJSot\nLHg95k9/gl9kpNlz1HlwASUiIjtd+PZbswkcAOx/7TVc+PZbJ0dE3iowPh5TZBnJM2Y0WwuxS3Iy\n7v30U0TfdpsLoyNnkTrxeA4l38aWPN6IU7vNY720xDpprrawEF9MnIjKy5ctlgns3t1tl3XoaLxe\nzOvoelEMBpSfO4ea4mJo/Pygi4+HT0hIh72fI/BaMS86Ohpo5Taj7E4lIrJDRX6+1QQOqF/WoSI/\n3yuTOHINyccHwb17g5343ondqUREdlCMRvvKmUwdHAkRUT0mcUREdgiIjLS5ZINWp0NAt25OioiI\nvB2TOCIiOwTGxGDI449bLTPkiScQGBPjpIiIyNsxiSMisoOiKOidno6ekyebPd9z8mT0njmTi/8S\nkdNwYgMRkZ38IiJw55tvImXuXPy4cmXjYr8pc+cirH9/+Hbp4uoQiciLMIkjImoFXVQUcMstiBo1\nCsbaWqh9fQEVOzWIyPmYxBERtYVKBbW/v6ujICIvxp+PRERERB6ISRwRERGRB2ISR0REROSBmMQR\nEREReSAmcUREREQeiEkcERERkQdiEkdERETkgZjEEREREXkgJnFEREREHohJHBEREZEHYhJHRERE\n5IGYxBERERF5ICZxRERERB6ISRwRERGRB2ISR0REROSBmMQREREReSAmcUREREQeiEkcERERkQdi\nEkdERETkgZjEEREREXkgJnFEREREHohJHBEREZEHYhJHRERE5IGYxBERERF5ICZxRERERB6ISRwR\nERGRB2ISR0REROSBmMQREREReSAmcUREREQeiEkcERERkQdiEkdERETkgZjEEREREXkgJnFERERE\nHohJHBEREZEH0rg6AAAQQswE8DKAfgDSZFk+1OTcswAeBlAH4AlZlre4JEgiIiIiN+IuLXHHAUwH\nsLPpQSFEPwAC9cnd3QD+IoSQnB8eERERkXtxiyROluUzsixnALgxQZsKYI0sy3WyLJ8DkAFguLPj\nIyIiInI3bpHEWdEDwIUmjy82HCMiIiLyak4bEyeE2AogsskhCYACYLEsy+stPM1c16ni6NiIiIiI\nPI3TkjhZlse14Wl5AGKbPI4BkG+uoBBiDIAxTd4P0dHRbXjLzk+n07k6BLfEemmJdWIe68U81ot5\nrJeWWCfmCSFebvJwhyzLO6w+QVEUt/mTnp7+XXp6+tAmj/unp6cfTk9P16anpyemp6dnpqenS3a+\n1suu/jzu+If1wnphnbBeWC+sF9aJ+/1pS724xZg4IcQ0IcQFADcD+FoIsQkAZFk+CUAGcBLARgCP\nybLM7lQiIiLyem6xTpwsy2sBrLVw7lUArzo3IiIiIiL35hYtcR1kh6sDcFM7XB2Am9rh6gDc0A5X\nB+Cmdrg6ADe1w9UBuKkdrg7ADe1wdQBuakdrnyApCnsniYiIiDxNZ26JIyIiIuq0mMQREREReSC3\nmNjgSEKI1wDcC6AWQBaAh2RZLms49yyAhwHUAXhCluUtLgvUiYQQMwG8jPo9aNNkWT7UcDwewCkA\npxuK7pVl+TGXBOkCluql4ZxXXis3EkK8BOARAFcaDj0ny/JmF4bkUkKIiQDeQv0P4A9lWV7i4pDc\nghDiHIBSACYABlmWvXJ7RCHEhwDuAVAgy/LAhmNhAD4FEA/gHAAhy3Kpy4J0Mgt14vX3FSFEDICV\nAKIAGAG8L8vy2629XjpjS9wWACmyLA9C/V6rzwKAEKI/AIH6L+y7AfxFCGFuR4jO6DiA6QB2mjmX\nKcvykIY/XpPANTBbL0KIfvDea8WcpU2uEa+60TYlhFABeBfABAApAO4XQvR1bVRuwwRgjCzLg701\ngWvwd9RfH039HsA2WZb7ANiOhu8kL2KuTgDeV+oA/EaW5f4ARgJY1HA/adX10umSOFmWt8mybGp4\nuBf1uzwAwBQAa2RZrpNl+RzqEzyvuNnIsnxGluUMmN/GzGuTEyv1MhVeeq1Y4LXXyA2GA8iQZfm8\nLMsGAGtQf61Q/TXS6b5PWkuW5e8BFN9weCqAjxr+/hGAaU4NysUs1Ang5fcVWZYvy7J8pOHvFajv\nFYtBK6+Xzv6f7mHULxIMAD0AXGhy7mLDMW+XIIQ4KIT4Tghxi6uDcRO8VppbJIQ4IoT4QAgR4upg\nXOjG6yIP3n1dNKUA+EYIcUAI8Yirg3Ez3WRZLgDqv7gBRLg4HnfB+0oDIUQCgEGob3iKbM314pFj\n4oQQWwFENjkkof4msliW5fUNZRajfmzG6iZlbtRp1lexp07MyAcQJ8tysRBiCIC1Qoj+Db8KOoU2\n1kunvlZuZK2OAPwFwCuyLCtCiP8BsBTAfOdH6Ra86rpopVGyLF8WQkQA2CqEONXQAkNkDu8rDYQQ\nQQA+R/3Y6wohRKvuKR6ZxMmyPM7aeSHEPACTANzR5HAegNgmj2NQn8R0CrbqxMJzDGho5pZl+ZAQ\nIgtAMoBDVp/oQdpSL+jk18qNWlFH7wOwlPh6gzwAcU0ed+rrojUaWgwgy3KhEOJL1Hc9M4mrVyCE\niJRluUAIEYWfBvN7LVmWC5s89Nr7ihBCg/oE7mNZlr9qONyq66XTdac2zB57GsAUWZZrm5xaB2C2\nEEIrhEgE0AvAflfE6GKNrQlCiPCGwdoQQvREfZ1kuyowF2vaysJrpUHDTeS6+wCccFUsbuAAgF5C\niHghhBbAbNRfK15NCBHQ0JoAIUQggPHw7utEQsv7yc8b/j4PwFc3PsELNKsT3lcarQBwUpblZU2O\ntep66XQ7NgghMgBoAVxrONS4bEbDshHzARjgRctGCCGmAXgHQDiAEgBHZFm+WwhxH4BXUF8fRgAv\nyrK80fIrdS6W6qXhnFdeKzcSQqxE/VgNE+qnuz96fbyGN2r4kbgMPy0x8kcXh+RyDT90vkR917IG\nwCfeWi9CiFUAxgDoCqAAwEuo3xf8M9S37ucCSJdlucRVMTqbhToZCy+/rwghRgPYhfpVEpSGP8+h\nvsFAhp3XS6dL4oiIiIi8QafrTiUiIiLyBkziiIiIiDwQkzgiIiIiD8QkjoiIiMgDMYkjIiIi8kBM\n4oiIiIg8EJM4IiIiIg/kkdtuERG5ihAiHcCTqF+sdJ8sy3fYeAoRUYdgEkdE1DrXALwJoC+a789M\nRORUTOKIiG7QsJfwAQB3yrJ8RAgRDeAogBmyLG9vKDPflTESEXFMHBHRDWRZzgbwNIBPhBD+AP4O\nYIUsy7tcGxkR0U+YxBERmSHL8ocAMgDsAxAJ4HnXRkRE1ByTOCIiyz4AkALgHVmWDa4OhoioKSZx\nRERmCCECAbwF4EMALwshQl0cEhFRM0ziiIjMexvAAVmWFwDYCGA5AAghVEIIXwA+ANRCCF8hBCeJ\nEZHT8cZDRHQDIcQUAOMBDGg49BsAh4UQ9wPQon6ig9JwrgrARwAednacROTdJEVRbJciIiIiIrfC\n7lQiIiIiD8QkjoiIiMgDMYkjIiIi8kBM4oiIiIg8EJM4IiIiIg/EJI6IiIjIAzGJIyIiIvJATOKI\niIiIPBCTOCIiIiIP9P9HggSv3Kgo1wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21972140d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], s=100, c=y);\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what would happen if we applied the perceptron classifier to this dataset?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "p = Perceptron(lr=0.1, n_iter=10)\n",
    "p.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.81000000000000005"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(p.predict(X), y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x219723c3e10>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DgsDlG6FW+DcJZUPApUFQeCjR0e53nR93fCo1bX5yorEQQowQgx5amj2f19Xe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IBwtx4cLS3FcRx8gQAZhkF49UrsiorjznXzdWuMb8BAls+Zx6Z3323y3JwePbjgwQcIz5nVbK8f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\nUCYiIiLiAv8ff34Am3TmK8IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21972375828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plot_decision_boundary(p, X, y)\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fortunately, there are ways to make the perceptron more powerful and ultimately create\n",
    "nonlinear decision boundaries."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<!--NAVIGATION-->\n",
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